where \(||A||^2={\rm tr}(A^{\rm t}A)\)  is the Frobenius norm and
\(P\)  is a permutation matrix, whose entries \(P_{ij}\in \lbrace 0,1\rbrace \)  satisfy
the constraints \(\sum _iP_{ij}=\sum _jP_{ij}=1\) . The objective function in
Equation (REF ) appeared for the first time
in the formulation of the quadratic assignment problem (QAP) [1]},
which is one of the most important problems in the field of combinatorial
optimization.
The QAP was initially introduced in economics to find the optimal
assignement (=optimal permutation in our language) of \(N\)  facilities
to \(N\)  locations, given the matrix of distances between pair of facilities
(=filter matrix \(A\) ) and a weight matrix quantifying the amount of goods
flowing between firms (=correlation matrix \(B\) ).
